Darren -
> When specifying stochastic designs there is a question about event
> probability. Assuming 3 events with equal probabilities is
> 1/3 1/3 1/3 the same as 1 1 1 for practical purposes?
Yes
> Let's say I specify a design with 2 trial types and a null event. The xX.X
> matrix is n x 3 columns, with column 3 being all 1's.
>
> Would the efficiency of this design be approximated by
>
> trace(xX.X(:,1:2)*xX.X(:,1:2)')-1 ??
Yes, though you might be more interested in the efficiency of your design
for one or more specific contrasts, given by:
trace(c'*inv(xX.X(:,1:2)'*xX.X(:,1:2))*c)^-1
where c is a matrix of contrasts. With short ISIs for example, the efficiency
of a differential [1; -1] contrast will be greater than that of a main
effect contrast [1; 1], and vice versa for long ISIs (>~15s, once a
reasonable highpass filter is applied).
> Have you found it useful to estimate designs repeatedly to get one that is
> more efficient?
This may not be a good idea, since optimising efficiency of a finite design
might lead to nonbalanced orderings of event-types (with short ISIs for
example, you are likely to find that your design begins to approximate a
blocked design, which is most efficient at short ISIs, but may not be
psychologically desirable).
Rik
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